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Plasma thrusters

SEMI N A R F O R T HE M A S T E R I N N U C L EA R , PA R T I CL E A N D AS T R O P H Y S I C S ,

DEPARTMEN T O F PH YS I C S , T EC H N I SC H E UN I VE R S I TÄT MÜN C H E N ,

GER M A N Y ( W S 201 5 / 2016)

BY TI Z I A N O F U LC ER I

Structure of the seminar

•Motivation

•Rocket principle and momentum equation

•Power, thrust, specific impulse

•Case analysis: Constant power and thrust, prescribed mission time

•Plasma thrusters as a subset of electric propulsion systems

•Physics of plasma propulsion

•HET (Hall Effect Thruster)

•MPD (Magnetoplasmadynamic) Thruster

•VASIMR (Variable Specific Impulse Magnetoplasma Rocket)

•ELF Thruster (Electrodeless Lorentz Force Thruster)

•Conclusions and prospects

•References

Motivation

Plasma thrusters are researched and developed as a solution for the

following fields of application:

•Precise trajectory corrections for satellites and/or probes

•In-space robotic probe propulsion (example ESA SMART-1)

•In-space manned spacecraft propulsion to Mars (proposed)

•Propulsion in outer Solar System (beyond Jupiter’s orbit)

All of which require (or will require) high fuel efficiency (see later: Isp),

long lifespan, and a small thruster mass.

Rocket principle and momentum equation

•p(t) = Total momentum of the system (rocket + propellant)

•M(t) = Mass of the rocket + mass of unexpended propellant or “wet mass”

•v(t) = Rocket velocity

•

= Mass flow of the propellant

•c(t) = Jet velocity

Thrust, Power, Specific Impulse

Thrust:

Calculating the thrust (accelerating force on the rocket structure) in a vacuum:

Total momentum change of the system (rocket + propellant) must be zero:

Thrust, Power, Specific Impulse

Kinetic power:

From the kinetic energy of the total system (rocket + propellant), we can calculate

the kinetic energy per unit time (kinetic power) of the exhaust jet:

Thrust, Power, Specific Impulse

PRIMARY POWER

SOURCE

Produces thermal or

electric power:

THRUSTER

Converts primary

power to kinetic

power of the

propellant with

efficiency :

EXHAUST JET

Produces the

acceleration of the

rocket:

A rocket propulsion system can be generally understood as follows:

Thrust, Power, Specific Impulse

Until now we have the following quantities:

•Thrust:

•Kinetic power:

We can define another useful quantity, specific impulse, which measures

how much momentum is produced per unit mass (or weight) of expended

propellant:

•

•

Where is the standard gravitational acceleration at sea

level.

The two definitions are interchangeable:

Case analysis: Constant power and thrust,

prescribed mission time

The can be calculated as follows:

This means also that

Electric thruster starting with mass , operating for a time , of jet speed , such as to

accomplish and equivalent (force-free) velocity change of .

We are looking for the final mass of the rocket (which is the mass at the end of the mission)

Plasma thrusters as a subset of electric

propulsion systems

Space propulsion

Chemical propulsion

Liquid propellant

Solid propellant

Hybrid

Electric propulsion

Electric thrusters

Electrothermal

thrusters (resisto-jet)

Arc-jet thrusters

Electromagnetic

thrusters

Ion thrusters

Plasma thrusters

HET

MPD

VASIMR

ELF

Others…

Physics of Plasma Propulsion

•We deal with thrust generation, so we are interested in the

momentum equation for each species j:

Physics of Plasma Propulsion

•For further analysis of the possible accelerating processes we make the

following assumptions:

•Only two fluids: ions and electrons

•Most important assumption: the working fluid (propellant) is an electrically conducting

medium which remains quasi-neutral

•The collision terms will therefore describe collisions between ions and electrons:

•Anisotropic component of the pressure tensor negligible, so that reduces to

•Ion and electron velocities can be related in terms of current as follows:

•Inertial term on the left side of the electron equation negligible due to small electron

mass

Physics of Plasma Propulsion

•Useful definitions:

•Conductivity:

•Hall parameter:

•Electron cyclotron frequency:

•The momentum conservation equations for the ionic and the electronic

components becomes:

Physics of Plasma Propulsion

•We can define the following useful quantity:

which represents the electric field in a reference frame in motion with

the average heavy particle flow plus the electron pressure gradient

contribution.

•We can rewrite the expression for the current:

which can be recognized as the generalized Ohm’s law (relationship

between the fields and the currents in a plasma)

Physics of Plasma Propulsion

•With further hypotheses we arrive at the following equation for the

motion of the working fluid:

•All types of plasma thrusters are based on one or more of the above

effects included in this equation:

•Arc-jet thrusters are totally based on pressure gradients

•Ion thrusters are based on an externally generated E-field

•MPD thrusters are based mainly on the collisional contribution from the

electron component

•HET thrusters are based on the self-consistent E-field associated with

the Hall effect

Hall Effect Thruster (HET)

Parameter

Value

Typical thrust

10

-80 mN

Typical specific impulse

1000

-8000 s

Typical power

1 kW to 100 kW

Efficiency

70

-80%

Hall Effect Thruster (HET)

Principle of operation

1. Steady-state Radial Magnetic Field (B) produced by electromagnets

(0.02-0.03 T)

2. Injection of positively ionized propellant (usually Xenon) and at the

same time emission of electrons from the cathode.

3. An axial electric field (E) arises because of the charge separation.

4. The electrons, having less inertia that the ions react faster to the E-

field and drift towards the propellant channel.

5. The electrons have now an axial velocity v, which is perpendicular to

the radial B-field.

6. The vxB force (“Hall effect” on currents, “Lorentz force” on particles)

traps the electrons on a circular path at the end of the propellant

channel (current density j), making them act as a suspended negative

electrode.

7. The ions are accelerated towards the electron cloud reaching

velocities in the order of 10 to 80 km/s, they neutralize and carry

momentum away providing thrust to the structure.

Magnetoplasmadynamic (MPD) thruster

Parameter

Value

Typical thrust

2.5

-25 N

Typical specific impulse

2000

s

Typical power

100

-500 kW

Efficiency

40

-60%

Magnetoplasmadynamic (MPD) thruster

Principle of operation

1. Voltage is applied between the central and the external

electrode

2. The propellant is injected between the two electrodes

3. The voltage between the electrodes is sufficient to ionize

the propellant and generate a discharge with a radially

directed current distribution

4. The radial current produces an azimuthal magnetic field B

5. The magnetic field B is perpendicular to the current by

which it is generated, this creates a jxB force density per

unit length of the discharge on both ions and electrons,

independent of the charge sign.

6. The ionized propellant is pushed away by the jxB force,

producing thrust on the structure

Variable Specific Impulse Magnetoplasma Rocket

(VASIMR)

Parameter

Value

Typical thrust

5 N

Typical specific impulse

5000

s (optimal)

Typical power (VX

-200)

200 kW

Efficiency

70%

Variable Specific Impulse Magnetoplasma Rocket

(VASIMR) –Principle of Operation

1. Propellant is injected in the ionization chamber

2. The Helicon antenna ionizes the propellant,

which becomes a plasma

3. Superconducting coils confine the plasma

The plasma is heated to about 1MK by an Ion

Cyclotron Frequency antenna

4. The hot plasma drifts toward the lower

magnetic field region away from the thruster

5. The reaction is felt on the structure as thrust

Electrodeless Lorentz Force (ELF) Thruster

Parameter

Value

Typical thrust

1N (pulsed)

Typical specific impulse

1000

-6000 s

Typical power

50kW (pulsed)

Efficiency

>50%

Electrodeless Lorentz Force (ELF) Thruster

Principle of Operation

•Electromagnets wound around the propellant

channel produce a steady-state axial magnetic field

decreasing in intensity in the outward direction

•Propellant is pre-ionized and injected in the

channel

•A Rotating Magnetic Field is produced by two pairs

of coils excited with two identical sinusoidal

waveforms which are out of phase by 90°

•The RMF, induces an azimutal electric current in the

propellant j_theta

•The RMF driven currents, coupled with the large

axial magnetic field gradient produced inside the

conically shaped flux-conserving thruster, produce

a large axial JθxBr force that accelerates the

plasmoid to high velocity. The axial force is thus

overwhelmingly determined by the driven Jθand

resultant Br rather than thermal expansion forces,

maximizing thrust efficiency.

Conclusions and prospects

•Plasma thrusters are a promising research field

•Some plasma thruster types already demonstrated their utility

•There is a wide range of methods, configurations and mechanisms to

accelerate a plasma propellant (we did not cover all of them)

•In the near future we should expect an increased interest in this kind

of technology

•The physics of this systems is not very well understood: this is an

opportunity for both applied and theoretical physics

Special: Fusion Plasma Thrusters

Fusion Driven Rocket (FDR)

Special: Fusion Plasma Thrusters

Flow-Stabilized Z-Pinch Fusion Space Thruster

“Specific impulses in the range of 10^6s and

thrust levels of 10^5 N are possible.”

References

•Lecture notes from the 2004 MIT course «Rocket Propulsion» by Prof. Manuel Martinez-Sanchez

•«Rocket and Spacecraft Propulsion» by Turner, Martin J. L. Chapters 2 and 6

•«Magnetoplasmadynamic Thrusters» fact sheet from NASA’s website

(http://www.nasa.gov/centers/glenn/about/fs22grc.html)

•«An analysis of current propulsion systems»

(http://currentpropulsionsystems.weebly.com/electromagnetic-propulsion-systems.html)

•«Fundamental scaling law for electric propulsion concepts» by M.Andreucci, L.Biagioni,

S.Marcuccio, F.Paganucci -Alta S.p.a., Pisa, Italy

•«Development Toward a Spaceflight Capable VASIMR Engine and SEP Applications» by J.P. Squire,

M.D.Carter, F.R. Chang Diaz, M.Giambusso, A.V.Ilin, C.S. Olsen –Ad Astra Rocket Company,

Webster, Texas, USA and E.A.Bering, III –University of Houston, Houston, Texas, USA

•«Pulsed Plasmoid Propulsion: The ELF Thruster» J.Slough and D.Kirtley –MSNW, Redmond, WA,

USA

•“The Fusion Driven Rocket” PI: J.Slough, A.Pancotti et. al.

•“Advanced Space Propulsion Based on the Flow-Stabilized Z-Pinch Fusion Concept” U.Shumlak

et. al. –Aerospace & Energetics Research Program, University of Washington, Seattle, WA, USA

(https://www.aa.washington.edu/research/ZaP/research/plasmaOverview)

Pictures

•http://www.popsci.com/technology/article/2010-10/123000-mph-plasma-

engine-could-finally-take-astronauts-mars

•http://www.engadget.com/2015/04/01/how-ion-thruster-technology-will-

power-future-nasa-missions/

•http://htx.pppl.gov/ht.html

•Title picture: http://www.irs.uni-

stuttgart.de/forschung/elektrische_raumfahrtantriebe/triebwerke/mpd-

tw/fremdfeldbeschl-tw/mpd-afmpd.html

•Index picture: http://web.stanford.edu/group/pdl/

•Alta Space (now part of Sitael) website: www.alta-space.com

•Ad Astra website: http://www.adastrarocket.com/aarc/

•MSNW space propulsion website: http://msnwllc.com/space-propulsion